{"paper":{"title":"Plug-In Classification of Drift Functions in Diffusion Processes Using Neural Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A plug-in classifier estimates class-specific drift functions of diffusion processes with neural networks to achieve explicit convergence rates for excess misclassification risk.","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Jiarong Fan, Yating Liu, Yuzhen Zhao","submitted_at":"2026-02-02T20:48:01Z","abstract_excerpt":"We study supervised multiclass classification for diffusion processes, where each class is characterized by a distinct drift function and trajectories are observed at discrete times. We first derive a multidimensional Bayes rule and then construct a plug-in classifier by estimating the class-specific drifts with neural networks. Under standard regularity assumptions, we establish convergence rates for the excess misclassification risk, making explicit the contributions of drift estimation, time discretization, and dimension. Our analysis also highlights the benefit of exploiting the diffusion "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Under standard regularity assumptions, we establish convergence rates for the excess misclassification risk, making explicit the contributions of drift estimation, time discretization, and dimension. Our analysis also highlights the benefit of exploiting the diffusion structure: the drift is learned from all observed increments, leading to sharper guarantees than direct trajectory-based neural classifiers.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"Standard regularity assumptions on the diffusion processes, drift functions, and neural network approximation capabilities hold, together with the requirement that drift functions admit a compositional structure for effective performance in higher dimensions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A neural-network plug-in classifier for multiclass diffusion processes achieves explicit convergence rates for excess misclassification risk by estimating class-specific drifts from discrete increments.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A plug-in classifier estimates class-specific drift functions of diffusion processes with neural networks to achieve explicit convergence rates for excess misclassification risk.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"296a5f60b7294f7c14819fd640a004737688e836f3b9b43a19de84f6614e490c"},"source":{"id":"2602.02791","kind":"arxiv","version":2},"verdict":{"id":"e1ddcaf9-3979-4b1d-959b-35a80bd191d2","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T08:00:04.352966Z","strongest_claim":"Under standard regularity assumptions, we establish convergence rates for the excess misclassification risk, making explicit the contributions of drift estimation, time discretization, and dimension. Our analysis also highlights the benefit of exploiting the diffusion structure: the drift is learned from all observed increments, leading to sharper guarantees than direct trajectory-based neural classifiers.","one_line_summary":"A neural-network plug-in classifier for multiclass diffusion processes achieves explicit convergence rates for excess misclassification risk by estimating class-specific drifts from discrete increments.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"Standard regularity assumptions on the diffusion processes, drift functions, and neural network approximation capabilities hold, together with the requirement that drift functions admit a compositional structure for effective performance in higher dimensions.","pith_extraction_headline":"A plug-in classifier estimates class-specific drift functions of diffusion processes with neural networks to achieve explicit convergence rates for excess misclassification risk."},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":1,"snapshot_sha256":"ea8baf11ed25fcd5413a9c6759f62664daa66ddd1c01f8028a154835bffe5272"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}